Multi-Agent Collaboration for PrSTL Specifications With Temporal Collective Counting Operators

We address the collaborative path planning problem for multi-agent systems with heterogeneous capabilities, subject to uncertainty and operating under complex task specifications. Conventional Probabilistic Signal Temporal Logic (PrSTL) frameworks exhibit significant limitations in describing multi-agent collaborative tasks with temporally cumulative properties. To address this challenge, we extend the PrSTL framework by introducing a Temporal Collective Counting Operator to characterize such spatio-temporal specifications. We then formulate the multi-agent collaborative planning problem under dynamics uncertainty as a Mixed-Integer Second-Order Cone Program. This formulation leverages PrSTL to specify tasks with cumulative temporal properties, while employing Polynomial Chaos Expansion to propagate uncertainty. Finally, we propose a constraint relaxation mechanism to address the conservatism introduced by formula transformations and probabilistic constraints' approximation.